Engineering Institute of Technology

Unit Name

ENGINEERING MATHEMATICS I

Unit Code

BSC101C

Unit Duration

1 Term (2 Terms for 24 week delivery*)

Award

Bachelor of Science (Engineering)

Duration 3 years

Year Level

One

Unit Creator/Reviewer

 

Core/Elective

Core

Pre/Co-requisites

Nil

Credit Points

3

Total Course Credit Points 81 (27 x 3)

Mode of Delivery

Online or on-campus.

Unit Workload

(Total student workload including “contact hours” = 10 hours per week; 5 hours per week for 24 week delivery)

Pre-recordings / Lecture – 1.5 hours (0.75 hours for 24 week delivery)

Tutorial – 1.5 hours

(0.75 hours for 24 week delivery)

Guided labs / Group work / Assessments – 2 hours (1 hour for 24 week delivery)

Personal Study recommended – 5 hours (2.5 hours for 24 week delivery)

  • This unit may be delivered over 24 weeks (2 Terms) because the nature of the content is deemed suitable (from a pedagogical perspective) for a longer duration than the standard 12 week (1 Term). In addition, these 24-week duration Units require half the student workload hours, 5 hours per week, which allows the total load to be kept at 15 hours per week when combined with a typical 10 hours per week, 12-week Unit. EIT has extensive data to demonstrate that if the load is higher than 15 hours per week the attrition rate for part time students dramatically increases.

    Unit Description and General Aims

    This unit introduces the student to core mathematical concepts, processes and techniques necessary to support subsequent studies in Engineering. These concepts include, but are not limited to, the properties and engineering applications of linear, quadratic, logarithmic and exponential functions. The unit commences with linear equations and goes on to cover varied subjects including inequalities, functions, trigonometry, sequences, series, variation, ratio, proportion, algebraic functions, trigonometric ratios, trigonometric functions and applications. It rounds off with an introduction to differentiation and integration, followed by vectors, complex numbers and matrices. The topics in this unit are structured in such a manner that the student will be able to solve problems related to engineering applications by using these mathematical techniques.

    Learning Outcomes

    On successful completion of this Unit, students are expected to be able to:

    1. Detail mathematical concepts related to linear and absolute value inequalities

    2. Solve linear and quadratic equations

    3. Comprehend and apply the basics of functions and logarithms

    4. Perform simple trigonometric calculations

    5. Evaluate concepts related to sequences, series, variation, ratio and proportion

    6. Solve algebraic equations

    7. Use trigonometric ratios to solve mathematical problems

    8. Apply vector principles

    9. Perform calculations involving complex numbers

    10. Use matrices and determinants to solve mathematical problems

      Professional Development

      Completing this unit may add to students professional development/competencies by:

      1. Fostering personal and professional skills and attributes in order to:

        1. Conduct work in a professionally diligent, accountable and ethical manner.

        2. Effectively use oral and written communication in personal and professional domains.

        3. Foster applicable creative thinking, critical thinking and problem solving skills.

        4. Develop initiative and engagement in lifelong learning and professional development.

        5. Enhance collaboration outcomes and performance in dynamic team roles.

        6. Effectively plan, organise, self-manage and manage others.

        7. Professionally utilise and manage information.

        8. Enhance technologist literacy and apply contextualised technologist skills.

      2. Enhance investigatory and research capabilities in order to:

        1. Develop an understanding of systematic, fundamental scientific, mathematic principles, numerical analysis techniques and statistics applicable to technologists.

        2. Access, evaluate and analyse information on technologist processes, procedures, investigations and the discernment of technologist knowledge development.

        3. Foster an in-depth understanding of specialist bodies of knowledge, computer science, engineering design practice and contextual factors applicable to technologists.

        4. Solve basic and open-ended engineering technologist problems.

        5. Understand the scope, principles, norms, accountabilities and bounds associated with sustainable engineering practice.

      3. Develop engineering application abilities in order to:

        1. Apply established engineering methods to broadly-defined technologist problem solving.

        2. Apply engineering technologist techniques, tool and resources.

        3. Apply systematic technologist synthesis and design processes.

        4. Systematically conduct and manage technologist projects, work assignments, testing and experimentation.

Engineers Australia

The Australian Engineering Stage 1 Competency Standards for Engineering Technologists, approved as of 2013. This table is referenced in the mapping of graduate attributes to learning outcomes and via the learning outcomes to student assessment.

Stage 1 Competencies and Elements of Competency

1.

Knowledge and Skill Base

1.1

Systematic, theory based understanding of the underpinning natural and physical sciences and the engineering fundamentals applicable to the technology domain.

1.2

Conceptual understanding of the, mathematics, numerical analysis, statistics, and computer and information sciences which underpin the technology domain.

1.3

In-depth understanding of specialist bodies of knowledge within the technology domain.

1.4

Discernment of knowledge development within the technology domain.

1.5

Knowledge of engineering design practice and contextual factors impacting the technology domain.

1.6

Understanding of the scope, principles, norms, accountabilities and bounds of sustainable engineering practice in the technology domain.

2.

Engineering Application Ability

2.1

Application of established engineering methods to broadly-defined problem solving within the technology domain.

2.2

Application of engineering techniques, tools and resources within the technology domain.

2.3

Application of systematic synthesis and design processes within the technology domain.

2.4

Application of systematic approaches to the conduct and management of projects within the technology domain.

3.

Professional and Personal Attributes

3.1

Ethical conduct and professional accountability.

3.2

Effective oral and written communication in professional and lay domains.

3.3

Creative, innovative and pro-active demeanour.

3.4

Professional use and management of information.

3.5

Orderly management of self and professional conduct.

3.6

Effective team membership and team leadership.

Graduate Attributes

Successfully completing this Unit will contribute to the recognition of attainment of the following graduate attributes aligned to the AQF Level 7 criteria, Engineers Australia Stage 1 Competency Standards for Engineering Technologists and the Sydney Accord:

Graduate Attributes

(Knowledge, Skills, Abilities, Professional and Personal Development)

EA Stage 1 Competencies

Learning Outcomes

A. Knowledge of Science and Engineering Fundamentals

A1. Breadth of knowledge of engineering and systematic, theory-based understanding of underlying principles, and depth of knowledge across one or more engineering sub- disciplines

1.1, 1.3

1, 2, 3, 4, 5, 6, 7,

8, 9, 10

A2. Knowledge of mathematical, statistical and computer sciences appropriate for engineering technology

1.2

1, 2, 3, 4, 5, 6, 7,

8, 9, 10

A3. Discernment of knowledge development within the technology domain

1.4

1, 2, 3, 4, 5, 6, 7,

8, 9, 10

A4. Knowledge of engineering design practice and contextual factors impacting the technology domain

1.5

 

B. Problem Solving, Critical Analysis and Judgement

B1. Ability to research, synthesise, evaluate and innovatively apply theoretical concepts, knowledge and approaches across diverse engineering technology contexts to effectively solve engineering problems

1.4, 2.1, 2.3

 

B2. Technical and project management skills to design complex systems and solutions in line with developments in engineering technology professional practice

2.1, 2.2, 2.3, 3.2

 

C. Effective Communication

C1. Cognitive and technical skills to investigate, analyse and organise information and ideas and to communicate those ideas clearly and fluently, in both written and spoken forms appropriate to the audience

3.2

 

C2. Ability to engage effectively and appropriately across a diverse range of cultures

3.2

 

D. Design and Project Management

D1. Apply systematic synthesis and design processes within the technology domain

2.1, 2.2, 2.3

 

D2. Apply systematic approaches to the conduct and management of projects within the technology domain

2.4

 

E. Accountability, Professional and Ethical Conduct

E1. Innovation in applying engineering technology, having regard to ethics and impacts including economic; social; environmental and sustainability

1.6, 3.1, 3.4

 

E2. Professional conduct, understanding and accountability in professional practice across diverse circumstances including team work, leadership and independent work

3.3, 3.4, 3.5, 3.6

 

Unit Competency and Learning Outcome Map

This table details the mapping of the unit graduate attributes to the unit learning outcomes and the Australian Engineering Stage 1 Competency Standards for the Engineering Technologist.

 

Graduate Attributes

A1

A2

A3

A4

B1

B2

C1

C2

D1

D2

E1

E2

Engineers Australia Stage 1 Competency Standards for Engineering Technologist

1.1

                     

1.2

 

                   

1.3

                     

1.4

   

 

             

1.5

     

               

1.6

                   

 

2.1

       

   

     

2.2

         

   

     

2.3

       

   

     

2.4

                 

   

3.1

                   

 

3.2

         

       

3.3

                     

3.4

                   

3.5

                     

3.6

                     

Unit Learning Outcomes

LO1

                 

LO2

                 

LO3

                 

LO4

                 

LO5

                 

LO6

                 

LO7

                 

LO8

                 

LO9

                 

LO10

                 

Student assessment

Assessment Type

When assessed

Weighting (% of total unit marks)

Learning Outcomes Assessed

Assessment 1

Type: Multi-choice test / Group work / Short answer questions

Example Topics: Arithmetic, Variation, Ratio and Proportion, Algebra, Simple Equations, Graphs, Simultaneous Equations, Trigonometry, Geometry, Quadratic equations

Students may be asked to provide solutions to simple problems on various topics.

Week 4

(Week 8 for 24 week delivery)

15%

2, 5, 6

Assessment 2

Type: Multi-choice test / Group work / Short answer questions

Example Topics: Sequences and Series, Logarithms exponentials and Inequalities, Trigonometric Functions and Formulae

Students may complete a quiz with MCQ type answers or solve some simple problems or solve problems using software.

Week 7

(Week 14 for 24 week delivery)

20%

1, 3, 5, 7

Assessment 3

Type: Multi-choice test / Group work / Short answer questions / Practical

Example Topic: Short problems on basic differentiation and integration and vectors

Week 10

(Week 20 for 24 week delivery)

20%

8

Assessment 4

Type: Examination Example Topic: All topics

An examination with a mix of detailed report type questions and/or simple numerical problems to be completed in 3 hours

Final Week

40%

1 to 10

Attendance / Tutorial Participation

Example: Presentation, discussion, group work, exercises, self-assessment/reflection, case study analysis, application.

Continuous

5%

1 to 10

Prescribed and Recommended readings

Suggested Textbook

  • Bird, J. Basic Engineering Mathematics, 6th edn, John Wiley & Sons, ISBN-13: 978-0- 415-66278-9.

    Reference Materials

  • Kreyszig, A 2012, Advanced Engineering Mathematics Student Solutions Manual, 10th edn, John Wiley & Sons, ISBN-13: 978-1118007402

  • Peer reviewed Journals

  • Knovel library: http://app.knovel.com

  • IDC Technologies publications

  • Other material and online collections as advised during the lectures

Unit Content

One topic is delivered per contact week, with the exception of part-time 24-week units, where one topic is delivered every two weeks.

Topic 1

Basic Mathematics Review 1 (Mathematics Equation Editor Tools)

(Arithmetic, Variation, Ratio and Proportion)

  1. BODMAS

  2. Scientific notation, engineering notation

  3. Ratios

  4. Rates

  5. Scale Diagrams

  6. Direct Variation

  7. Inverse Variation

(Algebra, Simple Equations, Graphs, Simultaneous Equations)

  1. Indices, Brackets, Factorization

  2. Solving simple linear equations

  3. Graphing – axes, straight lines, gradients, proportionality

  4. Simultaneous equations

Topic 2

Basic Mathematics Review 2 (Introductory Trigonometry)

  1. Angles

  2. Triangles

  3. Pythagoras

  4. Sine, cosine, tan

  5. Trigonometric Ratios

  6. Elevation and Depression

  7. Non Right Angle Triangles

  8. Circle – properties, arc length, equation

  9. Graphing circles and the unit circle

  10. Radians

  11. Trigonometric Identities

(Introductory Geometry)

  1. Common shapes

  2. Area of common and complex shapes

  3. Common 3D shapes

  4. Volume of common and complex 3D shapes

    Topic 3

    Quadratic equations

    1. Quadratic equations

    2. Quadratic graphs

    3. Factorization

    4. Completing the square

    5. Solving by formula

    6. Practical problems

Topic 4

Sequences and Series

  1. Sums vs sequences

  2. Simple series (progression)

  3. Arithmetic progression

  4. Geometric progression

  5. Pascal’s triangle

  6. Permutation and combination

  7. Binomial theorem

  8. Graphing progressions

  9. Power series

Topic 5

Logarithms exponentials and Inequalities

  1. Logarithmic expression

  2. Laws of logarithms

  3. Natural (Naperian, hyperbolic) logarithms

  4. Exponential functions

  5. Graphing exponential functions

  6. Logarithmic Equations

  7. Application of Logarithms and exponential functions

  8. Change of base

  9. Inequalities and absolute values

Topic 6

Trigonometric Functions and Formulae

  1. Trigonometric graphs

  2. Period, amplitude, cycle, frequency

  3. Lag and lead (phase displacement)

  4. Trigonometric identities and formulae

  5. Cartesian and polar coordinates

Topic 7

Introduction to differentiation

  1. Basic principles of differentiation

  2. Notation

  3. Gradient curves

  4. Differentiation of simple trigonometric functions

  5. Differentiation of simple function

  6. Rate of change

Topic 8

Introduction to integration

  1. Basic principles integration

  2. Standard integrals

  3. Area under a curve – calculation and graph

Topic 9

Vectors and Scalars

  1. Vectors and Scalars

  2. Vector notation

  3. Resolving vectors

  4. Relative velocity

  5. Vector Definitions and Components

  6. Operations with Vectors

  7. Vector Applications

  8. Laws of Sines and Cosines

Topic 10

Complex Numbers

  1. Imaginary numbers

  2. Arithmetic of complex numbers

  3. The Argand diagram and polar form of a complex number

  4. The exponential form of a complex number

  5. De Moivre's theorem

  6. Solving equations and finding roots of complex numbers

  7. Phasors

Topic 11

Matrices, determinants and multivariable functions 1

  1. Introduction to matrices

  2. Multiplication of matrices

  3. Determinants

  4. The inverse of a matrix

  5. Multivariable functions

  6. Multivariable calculus

  7. Vector valued functions

  8. Parameterization

Topic 12

Matrices, determinants and multivariable functions 2

  1. Matrix form trigonometric identities

  2. Cramer's rule

  3. Using the inverse matrix to solve simultaneous equations

  4. Gaussian elimination

  5. lterative techniques

  6. Exam revision

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